Position Velocity and acceleration
Position Time graph example:
- Position is location
- Displacement is the position over time
- Displacement/time = velocity
- Velocity/time = Acceleration
- When theres acceleration we know that theres a net force acting on the object
- Acceleration and net force always act in the same direction
Position Time graph example:
Velocity Time Graphs
- If there is a constant velocity then the forces on the object are all equal, but when there is acceleration then a force is overpowering
- Shows acceleration through the slope and a velocity that is consistently increasing shows a constant acceleration
- The slope is also the net force in the example below
Introduction to Displacement and Difference between Displacement and Distance
- Displacement
- Straight line distance from initial to final points
- Displacement has direction
- Symbol for displacement if Δx and means change in position
- Δx = Xf - Xi ( position final - position initial)
- Displacement can be negative
- It measures in any linear dimension (feet, kilometers, meters)
- Magnitude of displacement simply means amount of displacement with out direction "number of units"
- Distance
- Does not have direction
- Displacement does not equal distance
Ways to show Direction
Important notes about Displacement and Distance
- For displacement none of the middle stuff in a journey matter only initial and final points
- Distance traveled can never be smaller than the magnitude of the Displacement
- Distance traveled must be greater than the magnitude of displacement because the shortest distance between any two points is a straight line
Introduction to Velocity and speed and the difference between the two
- Velocity
- Symbol is "V"
- V = Δx/Δt = Xf - Xi/ tf-fi
- Velocity has magnitude and direction
- Example problem:
- Speed
- Speed = Distance / time
- Speed only has magnitude, no direction
- Speed is not the same as velocity
- Speed and velocity only have the same magnitude when they move in a straight line
Understanding and walking position as a function of a time graph
- position as a function of time
- Position as meters on y axis
- Position in seconds on x axis
- Slope = m = rise/run = Δy/Δx = change in position/ change in time = Velocity
- The slope of a position vs time graph is velocity
- Examples below:
Introduction to acceleration with examples
- Symbol for acceleration is "a"
- a = Δv/ Δt = Vf - Vi / tf - ti
- a = (m/s) / (s/1) = (m/s) x (1/s) = m/s^2
Introduction to Uniformly accelerated Motion
- Uniformly Accelerated Motion (UAM)
- The UAM is uniformed meaning a number that does not change
- An object that is moving with an acceleration thats is constant
- Although examples of this aren't perfect because of multiple variables, it is still close enough
The UAM Equations
- If you know 3 of the UAM variables, you can determine the other 2 unknown variables.
- 5 - Variables
- 4 - Equations
- 3 - Known variables
- 2 - Variables to find
- 1 - Happy physics student
Walking position, velocity and acceleration as a function of time graph
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Examples of corresponding position, velocity, and acceleration vs time graphs
Introduction to free fall and the acceleration due to gravity
- An object is falling freely if the only force acting on it is gravity
- In order for an object to be in free fall it cant touch any other object
- There can be no air resistance on an object in free fall
- When an object is in free fall on earth, ay = =g = -9,8 m/sˆ2
- g = acceleration due to gravity, g earth = 9.81 m/sˆ2
- Even though g is not constant throughout the world, 9.81 m/sˆ2 is the accepted value
- An object doesn't have t be moving downward to be in free fall
- The acceleration for an object in free fall is negative g, the acceleration on Earth is just g
- in terms of free fall the negative in the -g represents a downward direction to the force
- Gravity is not the same in all places in the world making it not constant in a global level, but in a local level the gravity is UAM
- Acceleration due to gravity is independent from the mass so a heavier object will not accelerate faster
Apollo feather and hammer drop example
Frame of Reference
- The motion of the person taking measurements will affect the interperation of the motion of the object being observed
- If a guy is riding a skateboard and throwing a ball. From the perspective of a bystander , the ball is going at a parabolic curve. From the perspective of the guy riding the board, the ball is going up then down
- All motion is relative to a frame of reference (observers viewpoint)
Relative motion example problems
Introduction to vector components
- dx tells us the direction by showing vector is horizontal
- The sign in front of the magnitude tells us if its in the positive or negative direction
- Make sure you calculator is in radian
Introduction to projectile motion
- When an object is flying through the air, with no air resistance, it is traveling in 2 dimensions
- You need to split your known variables into x direction and y direction because the equation of motion is different in each direction
- X direction
- ax = 0
- When an object is moving upwards or downwards then its a constant value of 0, but if in projectile motion then, constant rat eof non zero number
- vx = Δx/ Δt
- Must know 2 variables to solve
- Y direction
- free fall
- ay = -g = -9.81 m/sˆ2
- Can use the UAM equations
- Must know 3 of the UAM variables to find the other 2
- Note : Δt is scalar meaning if you solve for change in time you can plug in both directions equations this is because Δt is independent of direction
Demonstrating the components of projectile motion
- Horizontal component is constant velocity and vertical component is UAM
- As a ball rolls down a table the horizontal velocity should be constant
- As ball is thrown up in the air, it should slow down as it goes up and eventually reach v = 0 but then it should speed up as it goes down
- the resultant vector of a ball being thrown's velocity is the hypotenuse of the right triangle in the visual representation if the balls motion. As well as the sums of the x and y components using Pythagorean theorem.
- Acceleration is always constant of 9. 81 m/sˆ2 downward in the y direction, even when the object is going up
- the acceleration in the x direction is 0
Projectile example problem